That could be because of the right knee arthroscopy Vollmer underwent in late February; the problems he was having with the knee led to the right tackle struggling a bit down the stretch last season.

Before that, however, the 6-foot-8-inch native of Germany was playing at an extremely high level, allowing just one sack and 14 quarterback pressures through the first 10 games of the season. He missed Week 12, and when he returned a game later in Miami, he had arguably his worst outing of the season, allowing two sacks. According to profootballfocus.com, that was the first time in Vollmer’s career he had allowed two sacks in a game.

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Teams also may not be looking at Vollmer as a potential left tackle, which is the more high-profile of the two spots. He did start at left tackle for several games as a rookie because of an injury to Matt Light, but he has been on the right since.

The source said Vollmer does want to remain with the Patriots, who made him the 58th overall pick four years ago. But it is possible that Vollmer wanting to stay with New England has the team looking for a hometown discount-type deal.

If Vollmer re-signs, he will be the only one of the four second-round picks New England made that year who stays with the team beyond his rookie deal. Darius Butler was released during training camp in 2011, Ron Brace was cut late last season, and Patrick Chung signed with the Eagles as a free agent this month.

Vollmer was one of the best tackles slated to hit the free agent market, though two of them did not make it that far: Denver’s Ryan Clady and the Kansas City’s Branden Albert were franchised by their teams. Andre Smith is expected to return to the Bengals.

The only top tackle to switch teams is Jake Long, who left the Dolphins for St. Louis by signing a four-year contract worth as much as $36 million; he received $16 million guaranteed from the Rams.

Shalise Manza Young can be reached at syoung@globe.com. Follow her on Twitter @shalisemyoung. Greg A. Bedard of the Globe staff contributed to this report.

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